$\begingroup$To complement the excellent answers below, I'll give you an everyday example. A glass cutting board is harder than a kitchen knife. The cutting board will dull the knife. However, the cutting board is MUCH easier to break (less tough) than the knife.$\endgroup$
– JamesOct 17 '18 at 12:03

4 Answers
4

Hardness and toughness are very different qualities in materials and are weakly related.

Hardness is strongly related to the more well-defined quantity of stiffness which measures how easily a compound can be deformed under stress. Glass and diamond are very stiff materials, for example. If you try to poke them with something they resist deforming to accommodate your poke. (Hardness is not perfectly aligned to stiffness because of small scale microstructures in many materials, but this is good enough for now).

Toughness is a vaguer term for materials and there isn't a simple way to measure it. This is partially because it varies depending on circumstances in a way that stiffness does not and it is a property of the overall structure and not just the materials that make up the structure. Understanding it requires some insight into why things break (and why other things don't). we need to know a lot about the small scale structure of materials not just the substances involved. For example, stainless steel (used in knives and forks) is a well-known tough material but cast iron is brittle. Both are mostly made of iron. The differences are in the crystalline structures.

One key property of tough structures is that cracks don't propagate. So a stick of glass will break easily as will a glass fibre. But a bundle of glass fibres embedded in an epoxy resin can be very tough (because the cracks in individual glass fibres are not propagated through the epoxy resin). Some tough metals can adjust the micro defects in their crystalline structures to absorb the strain that would otherwise propagate cracks. Some very soft compounds are very tough because the deform so easily that it is hard to start cracks, nylon rope for example.

Diamond is very very stiff. But it has no protection mechanism against cracks. So, like glass, once a crack has started it doesn't take a lot of energy to cause it to spread, so it may be stiff but it isn't tough.

A fuller explanation of this took material scientists and engineers a long time to work out would require a whole book to do it justice. Luckily that book has been written and is called The New Science of Strong Materials. It is well worth a read.

$\begingroup$Definitely +1, but I preferred the full title given in the link ("The New Science of Strong Materials, Or Why You Don't Fall through the Floor") :)$\endgroup$
– tardigradeOct 15 '18 at 15:46

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$\begingroup$Toughness is well-defined: it's a measure of the amount of energy needed to cause a crack in the material to grow. And "hardness" isn't one measure, but (approximately) two: scratch hardness and indentation hardness. Diamond ranks very high on both hardness measures, but other materials (such as steel or rubber) can have very different scratch and indentation hardnesses.$\endgroup$
– MarkOct 15 '18 at 21:10

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$\begingroup$@mark You are right. But I was trying to simplify in a way that didn't require me to reproduce several chapters of Gordon's book on the subject. Toughness is complicated; hardness is simpler but not as simple as stiffness, but related.$\endgroup$
– matt_blackOct 15 '18 at 21:25

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$\begingroup$@Harshjain Toughness doesn't really work that way; it's mainly important in relation with how you want to use that particular material - e.g. do you want to hit other stuff with it? Hard or soft? Do you want to use it under tension? Torsion? Compression? Do you want it to hold a constant load forever, or do you get varying loads over time? At what kinds of temperatures and pressures, and what kinds of chemical environments? One reason that steel is such an awesome material (along with its low cost) is that we can make hundreds of kinds of steels for all kinds of purposes.$\endgroup$
– LuaanOct 16 '18 at 6:48

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$\begingroup$@Harshjain If you want the material that's toughest against being struck with a hammer against an anvil... try a pillow. If you want it to return back to its previous shape, many rubber-like materials work great - it very efficiently distributes the impact energy over a large volume. But neither of those is something you want to build skyscrapers with :)$\endgroup$
– LuaanOct 16 '18 at 6:52

Diamond has cleavage planes. If you want something nearly unbreakable, try nephrite, which is a tough form of jade used by the ancient Aztecs to make axe heads! Actinolite is another related "tough as steel" mineral. These minerals are made up of interlocking strands (actinolite) or microscopic fibers (nephrite). But diamond is a regular geometric lattice, so if you hit it at the right angle, it will break. Still, you can't make a scratch on glass with nephrite -- but diamond will do the job. That's because diamond is "harder" than glass (which is mostly silicon).

$\begingroup$True, but the detailed reason for the toughness of some minerals is complicated and related to the structure which takes a lot of background material to explain. even materials scientists took a good few years to get a grip on fracture mechanics.$\endgroup$
– matt_blackOct 15 '18 at 21:28

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$\begingroup$So, hardness means to scratch. So can Graphene scratch diamond and how can a machine hold 1 atom thick layer of garaphene$\endgroup$
– Harsh jainOct 16 '18 at 1:02

$\begingroup$Is there any known toughest substance$\endgroup$
– Harsh jainOct 16 '18 at 1:03

1

$\begingroup$@Harshjain There's two main kinds of hardness - scratch hardness, and indentation hardness. But of course, even those are just approximations. As for holding graphene, you can hold it in your hand. There's little special about handling it - don't think that just because it's "one atom thick layer" it will just cut through anything; it handles like any other fabric, mostly. The tricky bit with scratching diamonds with graphene is that graphene is flexible - it will tend to bend under pressure, and you need pressure to scratch things. But then, have you ever cut your hand on a sheet of paper? :)$\endgroup$
– LuaanOct 16 '18 at 7:06

If toughness is defined as the ability of object A to damage object B, then there's no such thing as the toughest object, let alone the toughest substance. For example, a steel saw can cut a block of wood in two. The very same block of wood, used as a hammer, can break a steel saw in two.

Even if we consider similar geometries, the type of damage would depend on the kind of action involved. A block of diamond would scratch a block of iron, and diamond vise would slowly flatten an iron block, while a fast impact would rather shatter diamond.

Also, you can easily flatten or break a small piece of steel with a steel hammer.

I haven't read all the answers that have been written, but the ones I have read are very good.

This is going to be a simple one:
Yes indeed, Diamond is the hardest substance known and it refers to the resistance to be scratched. In other words, try using a metal point to scratch it and it won't be possible. While you can use diamond to scratch or indent other substances.

It does not mean that it can't be destroyed with a heavy blow, the resistance to this has another name and diamond does not possess it.
It all is reduced to the type of solid in which it crystallizes, normally a stiff and not flexible crystal lattice becomes brittle, easy to break. But as it is very dense, small distance between atoms and or ions, it does not allow penetration.

Thank you for your interest in this question.
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